General Point Sampling with Adaptive Density and Correlations
R. Roveri, A. C. Öztireli, M. Gross
Proceedings of Eurographics (Lyon, France, April 24-28, 2017), Computer Graphics Forum, vol. 36, no. 2, pp. 107-117
Abstract
Analyzing and generating sampling patterns are fundamental problems for many applications in computer graphics. Ideally,
point patterns should conform to the problem at hand with spatially adaptive density and correlations. Although there exist ex-
cellent algorithms that can generate point distributions with spatially adaptive density or anisotropy, the pair-wise correlation
model, blue noise being the most common, is assumed to be constant throughout the space. Analogously, by relying on possibly
modulated pair-wise difference vectors, the analysis methods are designed to study only such spatially constant correlations. In
this paper, we present the first techniques to analyze and synthesize point patterns with adaptive density and correlations. This
provides a comprehensive framework for understanding and utilizing general point sampling. Starting from fundamental mea-
sures from stochastic point processes, we propose an analysis framework for general distributions, and a novel synthesis algo-
rithm that can generate point distributions with spatio-temporally adaptive density and correlations based on a locally station-
ary point process model. Our techniques also extend to general metric spaces. We illustrate the utility of the new techniques on
the analysis and synthesis of real-world distributions, image reconstruction, spatio-temporal stippling, and geometry sampling.
